$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 3x - 2$ and $ BC = 6x - 5$ Find $AC$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {3x - 2} = {6x - 5}$ Solve for $x$ $ -3x = -3$ $ x = 1$ Substitute $1$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 3({1}) - 2$ $ BC = 6({1}) - 5$ $ AB = 3 - 2$ $ BC = 6 - 5$ $ AB = 1$ $ BC = 1$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {1} + {1}$ $ AC = 2$